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Popular >

simplify ln(ate^{ct})

Solution

simplify

ln (a t e^{c t})

Solution

ln (a) + ln (t) + t c

Solution steps

ln (a t e^{c t})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (a t e^{c t}) = ln (a) + ln (t) + ln (e^{c t})

= ln (a) + ln (t) + ln (e^{t c})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{c t}) = c t ln (e)

= ln (a) + ln (t) + c t ln (e)

c t ln (e) = t c

= ln (a) + ln (t) + t c

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Frequently Asked Questions (FAQ)

What is ln(ate^{ct}) ?
The solution to ln(ate^{ct}) is ln(a)+ln(t)+tc